Chapter 4: Q 4.90 (page 447)

Evaluate the determinant
(a)
$[\begin{matrix} - 1 & 3 \\ - 2 & 4 \end{matrix}] (b) [\begin{matrix} - 7 & - 3 \\ - 5 & 0 \end{matrix}]$

Short Answer

Expert verified

Part (a). The value of the determinant is 2.

Part (b). The value of the determinant is -15.

Step by step solution

Part (a) Step 1. Given information

The given determinant is $[\begin{matrix} - 1 & 3 \\ - 2 & 4 \end{matrix}]$

Part (a) Step 2. Calculation

Firstly write the determinant

$[\begin{matrix} - 1 & 3 \\ - 2 & 4 \end{matrix}]$

Subtract the products of the diagonals

$= (- 1 \times 4) - (3 \times - 2) = - 4 - (- 6) = 2$

Hence the determinant value is 2.

Part (b) Step 1. Given information.

The given determinant is $[\begin{matrix} - 7 & - 3 \\ - 5 & 0 \end{matrix}]$

Part (b) Step 2. Calculation.

Firstly write the determinant

$[\begin{matrix} - 7 & - 3 \\ - 5 & 0 \end{matrix}]$

Subtract the products of the diagonals,

localid="1645170808775" $= (- 7 \times 0) - (- 3 \times - 5) = 0 - (15) = - 15$

Hence the determinant value is -15.

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Evaluate the determinant
(a)
$[\begin{matrix} - 1 & 3 \\ - 2 & 4 \end{matrix}] (b) [\begin{matrix} - 7 & - 3 \\ - 5 & 0 \end{matrix}]$

Short Answer

Step by step solution

Part (a) Step 1. Given information

Part (a) Step 2. Calculation

Part (b) Step 1. Given information.

Part (b) Step 2. Calculation.

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Evaluate the determinant(a)-13-24(b)-7-3-50

Short Answer

Step by step solution

Part (a) Step 1. Given information

Part (a) Step 2. Calculation

Part (b) Step 1. Given information.

Part (b) Step 2. Calculation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

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Evaluate the determinant
(a)
$[\begin{matrix} - 1 & 3 \\ - 2 & 4 \end{matrix}] (b) [\begin{matrix} - 7 & - 3 \\ - 5 & 0 \end{matrix}]$